We construct a minimal automaton for an output-incomplete Moore automaton. The approach is motivated by physical interpretation of seeing deterministic nite automata as models for elementary particles. When compared to some classical methods our minimal automaton is unique up to an isomorphism and preserves also the unde ned or unspeci ed behaviour of the original automaton.

This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under...

Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT ). The AT automaton has two quotients considered: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT , the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the par...

A deterministic finite automaton A is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton A to a particular one. We prove that it is a PSPACEcomplete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.

We prove that the limit dynamics of any finite automata network under parallel update schedule correspond exactly to fixed points a so-called strictly one-way cellular automaton. This correspondence is proven be exact, as automaton can transformed into corresponding network, latter former. transformation operated using output functions, which have been developed in author’s previous works.